1. Field of the Invention (Technical Field)
The present invention relates to optical absorption spectroscopy, particularly over an extreme dynamic range of concentrations.
2. Description of Related Art
Note that the following discussion refers to a number of publications by author(s) and year of publication, and that due to recent publication dates certain publications are not to be considered as prior art vis-a-vis the present invention. Discussion of such publications herein is given for more complete background and is not to be construed as an admission that such publications are prior art for patentability determination purposes.
Optical absorption spectroscopy can be used for quantitative measurements of the concentrations or number densities of gases, liquids, and solids. The underlying theory, identified as Beer's Law or the Beer-Lambert Law, relates the change in intensity of a light beam as it passes through a sample to the sample's optical absorbance:
      I          I      0        =      e                  -        n            ⁢                          ⁢      σ      ⁢                          ⁢      l      where I is the light beam intensity after passing through the sample, I0 is the light beam intensity before encountering the sample, n is the target species concentration or number density, σ is the species absorption cross section, and l is the length of the optical path through the sample. The ratio I/I0 is the transmission, and is expressed as a fraction between 0 and 1, or as a percentage between 0 and 100%. The product, nσl, is the optical absorbance, α, and is a dimensionless quantity. The target species concentration or number density, n, is readily determined from a measured sample absorbance, α, because the absorption cross section, σ, is a physical property of the target species and can be determined prior to investigating the sample, and the optical path length, l, is a design parameter of the optical absorbance measuring apparatus. Such types of apparatus include but are not limited to spectrometers including laser based spectrometers and spectrophotometers. The concentration can also be expressed as a mole fraction.
The measurement dynamic range, D, is the ratio of the largest absorbance that can be measured reliably, αMAX, to the smallest absorbance that can be measured reliably, αMIN; D=αMAX/αMIN. For fixed optical path lengths, D also determines the range of concentration or number density that can be measured. The largest measurable absorbance, αMAX, is, in part, limited by the smallest value of I that can be distinguished from zero. For example, an absorbance of 10 corresponds to only e−10=0.005% of the incident light exiting from the sample. Furthermore, reliably distinguishing an absorbance of 10 from absorbances of 9 or 11 requires distinguishing 0.002% transmission from 0.012% and 0.005% transmission, respectively. The requirements are further constrained by the need to also measure I0 when it is 20,000 times larger than I. Few optical detectors can operate over that range of light intensity. It would be possible to combine multiple detectors, each having a different sensitivity range, to cover the full absorbance dynamic range; but, this combination would be expensive to implement and likely to need frequent calibration.
Samples having large absorbances, i.e., α>>1, are identified as optically thick or optically dense. The terms are used interchangeably. A complete description of the spectroscopy of optically thick samples requires an elaboration of Beer's Law to include the shape of the absorption feature,α(ν)=S(T)·g(ν,T,P,χi)·n·l, where < is the optical frequency (inversely proportional to wavelength), S is the line strength, T the temperature, P the pressure, and Oi the species mole fraction. The line shape function, g, is a maximum at the center of the absorption line and is a Voigt function for most gases near atmospheric pressure. The Voigt function is a convolution of Doppler and Lorentzian line shapes as is well known in the art. Numerical methods for computing Voigt functions are given by Drayson (S. R. Drayson, “Rapid Computation of the Voigt Profile,” J. Quant. Specrosc. Radiat. Transfer 16, 611-614 (1976)) and Hui et al. (A. K. Hui, B. H. Armstrong, and A. A. Wray, “Rapid Computation of the Voigt and Complex Error Functions,” J. Quant. Spectrosc. Radiat. Transfer 19, 509-516 (1978)). FIG. 1 is a series of transmission spectra showing the effect of increasing peak absorbances. The spectra were calculated using the HITRAN data base (Rothman, L. S., Jacquemart, D., et al., “The HITRAN 2004 Molecular Database,” J. Quant. Specrosc. Radiat. Trans. 92, 139-204 (2005)) to simulate the methane absorption line at 1654 nm, and assume a 1 m long optical path. At the lowest methane concentration 10 corresponding to the average ambient atmospheric methane concentration, 1.7 ppm, the transmission appears to be 1.0 for all wavelengths. The absorbance, 3.7H 10−5, corresponds to a transmission of 0.99996 at line center and cannot be observed on the scale of the figure. Increasing the concentration to 10%, trace 14, increases the absorbance to 2.1, and the transmission is only 13%. By 50% the sample is optically thick, trace 16; the peak absorbance is 10.9 and the transmission reduced to nearly zero at 0.000019. Increasing the concentration further to 100% broadens the transmission line shape 18 and widens the wavelength region over which the sample is optically thick.
Hirshfeld describes one approach for obtaining quantitative absorption spectra of optically thick samples (T. Hirschfeld, “Dynamic range improvement in Fourier transform infrared spectroscopy,” J. Am. Chem. Soc. 50, 1227-1228 (1978)). He teaches simultaneous measurements of a given sample using two different path lengths to solve the problem of optically dense samples. Garver et al. describes a spectrometer having a plurality of path lengths (T. M. Garver, D. G. Jenkins, and A. Riser, “Multiple pathlength spectrometer,” U.S. Pat. No. 6,643,016, issued Nov. 4, 2003), with each path length illuminated by light having a narrow wavelength range and the length optimized for the anticipated absorbance within that wavelength range.
Sample cells having widely variable path lengths are commercially available. Examples include the model A134 gas cell from Bruker Optics that can be adjusted for optical paths between 3.2 and 40 m. The cell uses White's design (White, J. U., “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am., vol. 32, pp 285-288 (May 1942)) for a multiple pass optical cell, and is expensive and requires careful adjustment to change the optical path length. Accessories for Perkin Elmer's BX series of Fourier transform infrared spectrometers include Teflon spacers available in thicknesses between 0.025 and 0.5 mm that are used to define the optical path length between entrance and exit windows. Changing the path length, however, requires first removing the sample and dismantling the cell.
A sub-specialty of optical spectroscopy known as saturation spectroscopy (S. Svanberg, G.-Y. Tan, T. P. Duffey, W.-M. Du, T. W. Hansch and A. L. Schawlow, “Saturation spectroscopy for optically thick atomic samples,” J. Opt. Soc. Am. B 4, 462-469 (1987); H. Chen, H. Li, Y. V. Rostovtsev, M. A. Gubin, V. A. Sautenkov, and M. O. Scully, “Near-infrared saturation spectroscopy of cesium molecules using a diode laser,” J. Opt. Soc. Am. B 23, 723-726 (2006)) is a non-linear spectroscopic technique for investigating fine structure in atomic spectra and takes advantage of unusual optical properties of optically thick gaseous samples. This approach is not suitable for molecular species, nor does it provide quantitative information about species concentrations or number densities.
At the other extreme, the minimum detectable absorbance, αMIN, is determined by the largest value of I that can be reliably distinguished from I0. For nearly all light sources, including lasers and lamps, distinguishing I from I0 is limited by the amplitude noise of the light source. This noise is commonly known as excess noise, pink noise, source noise, and 1/f noise. The noise power spectrum maximizes at frequencies near DC, and decreases with increasing frequency until fundamental noise sources including laser-detector shot noise and detector thermal noise are dominant. Researchers, including the Inventors, have demonstrated spectroscopic techniques that minimize the deleterious effects of excess noise by shifting the measurement bandwidth from frequencies near DC to those where excess noise is unimportant. Minimum detectable absorbances of αMIN. 10−5 for a one second measurement are typically achieved using wavelength tunable, continuous wave diode lasers as light sources. Pertinent techniques include wavelength modulation spectroscopy (J. Reid, M. El-Sherbiny, B. K. Garside, and E. A. Ballik, “Sensitive limits of a tunable diode laser spectrometer with application to the detection of NO2 at the 100-ppt level,” Appl. Opt. 19 3349 (1980); J. A. Silver, “Frequency Modulation Spectroscopy for Trace Species Detection: Theory and Comparison Among Experimental Methods,” Appl. Opt. 31, 707 (1992); and, D. S. Bomse, A. C. Stanton and J. A. Silver, “Frequency Modulation and Wavelength Modulation Spectroscopies: Comparison of Experimental Methods Using a Lead-Salt Diode Laser,” Appl. Opt. 31, 718 (1992)), frequency modulation spectroscopy (G. C. Bjorklund, “Method and device for detecting a specific spectral feature,” U.S. Pat. No. 4,297,035, issued Oct. 27, 1981; G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983)), two-tone frequency modulation spectroscopy (“Frequency modulation spectroscopy using dual frequency modulation and detection,” U.S. Pat. No. 4,765,736; issued Aug. 23, 1988; D. E. Cooper and T. F. Gallagher, “Double Frequency Modulation Spectroscopy”, Appl. Opt. 24, 1327-1333 (1985); J. A. Silver and A. C. Stanton, “Two-Tone Optical Heterodyne Spectroscopy Using Buried Double Heterostructure Lead-Salt Diode Lasers,” Appl. Opt. 27, 4438 (1988)), rapid scan absorption spectroscopy (Aerodyne), and noise canceller methods (P. C. D. Hobbs, “Noise cancelling circuitry for optical systems with signal dividing and combining means,” U.S. Pat. No. 5,134,276, issued Jul. 28, 1992; P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. 36, 903 (1997)).
The high sensitivity techniques assume absorbances small enough that Beer's Law can be approximated as follows:
                                          Δ            ⁢                                                  ⁢            I                                I            0                          =                              (                                                            I                  0                                -                I                                            I                0                                      )                    ⁢                    =                      1            -                          exp              ⁡                              (                                  -                  α                                )                                                                                    ⁢                  ≈                      α            ⁢                                                  ⁢                          (                              for                ⁢                                                                  ⁢                α                ⁢                                  <<                  1                                            )                                          In this case, the absorbance, α, is linearly proportional to n, the target species number density or concentration. Non-linearities become important as a exceeds ˜0.1. FIG. 2 shows changes in wavelength modulation spectral line shapes using second harmonic (2f) detection for methane as the methane concentration increases. Amplitudes are scaled to unity. The spectra were calculated using HITRAN data base information and follow the procedure described by Silver (1992), and assume a 1 m optical path length. At the ambient atmospheric methane concentration, 1.7 ppm, the absorbance is 3.7 H 10−5, and the spectral line shape 30 looks similar in shape to the second derivative of the absorption line. The extremum 32 in the 2f spectrum occurs at the absorption line center. The 2f line shape remains nearly invariant (although the magnitude would increase) for concentrations up to about 1.6%, 38, corresponding to an optical absorbance of 0.35. Increasing the concentration by an additional order of magnitude results in a broader central peak and shallow side lobes 40. As the sample becomes optically thick (α=10.5), there is nearly no light transmitted at the peak center, and the central lobe of the 2f spectrum disappears 44 leaving a significantly different spectral line shape 42. The 2f signal magnitudes are linearly proportional to concentration for α<0.1, and become sub-linear at higher concentrations and at the highest concentrations are no longer monotonic. The non-linearity is strongest among spectra 38, 40, and 42. Increasing the methane concentration form 1.6% to 10%, a factor of 6.25, increases the 2f extremum by only 0.15. The next increase, from 10% to 30%, actually produces a drop in 2f magnitude as the largest parts of spectral line 42, the two side lobes, are half the size of the central lobe in the 10% concentration spectrum 40.
An embodiment of the instant invention is a natural gas leak detector having a methane concentration measurement range extending from the ambient atmospheric background concentration of about 1.7 parts per million to 100%. No known prior art exists in the areas of methane concentration measurements or natural gas leak detection that encompasses a similarly large measurement dynamic range. Griggs et al. (M. Griggs, L. L. Action, and G. D. Hall, “Method and apparatus for accurate remote monitoring of gases,” U.S. Pat. No. 4,520,265, issued May 28, 1985) describe optical measurements using a narrow band optical interference filter centered at the Q-branch of the methane band at 3.3 μm that is combined with gas correlation cells and a separate measurement of light intensity at 10 μm to determine methane average concentrations along an open path in order to identify methane plumes resulting from natural gas leaks. The light source is thermal emission from background terrain or buildings. Applications include open path measurements from airborne platforms or ground vehicles. The largest optical absorbance is about 6. Although Griggs describes the interference filter as “narrow band,” its wavelength pass band is large compared with the width of methane absorption lines having absorbances below ˜2.
Heath Consultants, Inc. (Houston, Tex.) sells two optical methane sensors. Their Optical Methane Detector or OMDJ has a fixed open path approximately 1 meter long that has a manufacturer's stated measurement range of 1 to 200 ppm. This dynamic range is 5000 times smaller than the dynamic range of the instant invention. The other, called Remote Methane Leak Detector or RMLDJ, is a hand-held, point-and-shoot, diode laser based device with a measurement range of 0 to 99,999 ppm-m. The unit ppm-m is known as column density and is the product of the average gas concentration along an optical path and the optical path length; i.e., it is the product nl. Rutherford (J. M. Rutherford, “Method and apparatus for laser-based remote methane leak detection,” U.S. Pat. No. 7,075,653; issued Jul. 11, 2006) describes the RMLDJ. The instrument uses only one spectroscopic method, wavelength modulation spectroscopy, and employs an open optical path of varying length. A handheld optical transceiver emits light from a near-infrared diode laser (nominal wavelength 1654 nm) and collects light that is back scattered from or reflected from an object illuminated by the outgoing beam. The optical path length is double the distance from the transceiver to the object. This length changes as the operator moves the transceiver. A visible laser beam aligned with the near-infrared laser helps the operator to determine the location of the near-infrared beam. Changes in the optical path length result in concomitant changes in the methane column density due to the integrated absorbance by atmospheric background methane alone the optical path. Data analysis methods emphasize identifying sudden changes in methane column density exceeding the signal due to the background concentration as indicative of a natural gas leak. In contrast, the instant invention samples gas into an optical cell having a fixed and constant optical path length, and measures absolute methane concentrations between nominally 1.7 ppm and 100%. The present invention does not rely on changes in column density where the starting column density is uncertain.
In favorable cases, it is possible to use two or more spectral features having substantially different line strengths to span a large dynamic range as demonstrated by Zondlo et al. (Zondlo, M. A., J. A. Silver, D. S. Bomse, and M. E. Paige, “VCSEL-based hygrometer for the High-performance Instrumented Airborne Platform for Environmental Research (HIAPER)”, American Chemical Society National Meeting, Paper No. 302, Analytical Chemistry, Analytical Chemistry in the Atmospheric Sciences, Mar. 14, 2005, San Diego, Calif.) for atmospheric water vapor measurements. Zondlo's approach does, however, require a highly prescribed combination of target species spectroscopic properties, light source wavelength coverage, and freedom from interfering species. These requirements are more easily met for water vapor than for other species because water vapor occurs at relatively high concentrations and has a plethora of absorption bands throughout the mid- and near-infrared wavelength regions.
Currently used natural gas leak detection methods employ up to three separate devices to span natural gas concentrations from ˜1 ppm to 100%. The technology includes high- and low-sensitivity flame ionization detectors, and a thermal conductivity measurement for the largest concentrations.